Wrapping it up

Well, the semester of Math for Elementary Teachers is wrapping up this week! You would think after all the math classes I have taken, I wouldn't have anything else to learn. But, your wrong. I can not believe all the great skills, information, and techniques I learned this year. Out of all the different things I learned this year, the one thing that always came back to me was all the new techniques that are out there today that I never learned when I was in grade school. The new "ways" seem so much more engaging and easier to understand. Its great that they have come up with so many different ways to figure out one problem, because what works for some...doesn't always work for others. I do believe it is important to not forget about the older techniques as we are teaching the new ones though. There were many different times in grade school when I couldn't understand a problem and my dad helped me understand it with techniques that he learned when he was in school! So, remember as great as the new techniques seem, the old ones can be just as great!

Another important part of this class was learning about how important it is to keep your students engaged. I found this great video on youtube of a teacher showing different techniques he uses in a high school math classroom to keep his students engaged throughout the lesson. I believe the techniques used in this video can be used with any age group.

Here is another useful video on keeping your students engaged in a first grade math classroom. I think that using hand gestures, repeating, working with partners, etc. are a great way to keep your students engaged and following the rules. This video shows exactly that....

So, lets make a pact as teachers, parents, mentors, etc that we will work to keep our students or children engaged in learning so that it can be an exciting experience for both them and yourself.

To end this blog, here is a great website that lists different tips/techniques to keep children engaged in a classroom. Remember, not only can teachers use these techniques in the classroom but parents can also use these techniques at home.

http://www.edutopia.org/classroom-student-participation-tips

Fractions - why are they important?!

Whenever the unit of fractions comes up, I always go into a little panic. I understand the concept of fractions but I always get confused when it comes to adding, subtracting, multiplying, and dividing fractions. There are so many different steps to each problem that it confuses me. Multiplying and dividing fractions is always the most confusing to me, but once I learned the different properties it all became a lot easier to me.

Here is a great example of some of the basic properties for multiplication of rational numbers:

Here is a website about why equivalent fractions are important and the steps to working them out. It goes over the theorem, adding, subtracting, multiplying, dividing, and formulas.

http://www.cccoe.k12.ca.us/edsvcs/commoncore/summit/HWu/importance_of_equivalent_fractions.pdf

Now, we think...why is it important to learn about multiplying and dividing fractions? I'll give you a great example.

My husband and I have this great rhubarb plant in our back yard and it keeps growing and growing. I found a great recipe for a rhubarb cake that I wanted to make for my husband but I only needed to make half a recipe considering it was just my husband and I eating it. I had to cut the whole recipe in HALF! Now, before this chapter...I would not have known how to do this. Here is the recipe: (the part in parentheses is the 1/2 version)

1/4 cup butter, softened (1/8 cup)
1 1/2 cups brown sugar packed (3/4 cup)
1 egg (1/2 egg)
1 teaspoon pure vanilla extract (1/2 teaspoon)
1 1/2 cups flour (3/4 cup)
1 teaspoon baking powder (1/2 teaspoon)
1/8 teaspoon salt (1/4 teaspoon)
1 cup dairy sour cream (1/2 cup)
4 cups fresh rhubarb cut into 1/2 inch pieces (2 cups)

1/3 cup granulated sugar (1/6 cup)
1/2 teaspoon freshly grated nutmeg (1/4 teaspoon)

Preheat oven to 375 degrees
Line a greased 8 x 5 (I used 4 x 4) pan with parchment paper.
Beat butter and brown sugar in a bowl until creamy. Beat in egg and vanilla.
In another bowl, mix flour, baking powder, and salt. Stir into creamed mixture alternately with sour cream. Stir in rhubarb. Pour mix into pan.

Mix sugar with nutmeg. Sprinkle over batter. Bake 40 minutes (took about 30). Cool in pan for 30 minutes, remove from pan to a cooling rack. Refrigerate leftovers.

Now, you see if I didn't know how to divide fractions I would have had to eat this whole cake! (not that it would be a bad thing) But, this made it a lot more reasonable for a household of 2. I hope you enjoy the recipe, let me know what you think!

GCF and LCM

This week when looking through the book and starting my homework, I was at the same daze I always am when it comes to finding the greatest common factor and least common multiple. I always seem to get the two confused with each other! After reading through the book more and doing some of the examples I definitely understand the information a lot better. A few of the things that helped me (and that can hopefully help you) were to have the definitions in front of me, examples to look back at, and the steps to refer to.

Greatest Common Factor - the greatest natural number that is a factor of both numbers. (Also known as the greatest common divisor, GCD)

Example: Finding the GCF of 24 and 30.
                 A= the set of factors of 24= {1,2,3,4,6,8,12,24}
                 B= the set of factors of 30= {1,2,3,5,6,10,15,30}
                 The set of common factors of 24 and 30 = {1,2,3,6}
                 ANSWER: 6 is the GCF of 24 and 30.

Least Common Multiple - the smallest natural number that is a multiple of both the natural numbers.

Example: Finding the LCM of 6 and 8.
                C= the set of multiples of 6= {0,6,12,24,30,36,42,48....}
                D= the set of multiples of 8= {0,8,16,24,32,40,48,56,64....}
                The set of multiples of 6 and 8 = {0,24,48..}
                ANSWER: 24 is the LCM of 6 and 8.

I found a great website that gives you step by step instructions on finding the GCF and LCM. It gives great examples and understanding. I hope this website is as useful to you as it was to me!

http://www.purplemath.com/modules/lcm_gcf.htm

After going through these definitions and examples finding the GCF and LCM was like riding a bike... I will remember how to do it now and years down the road. I hope this information helps you as much as it helped me!

Lattice method...say what?!

Hello! Ever hear about the lattice method? I never have until my fourth year in college! But, it truly is a great method for multiplying, especially larger numbers!!! This is what a lattice method looks like:

Looks confusing, doesn't it?! But, in reality, it is a great method! I am going to share a few of the steps with you to clarify how easy the lattice method really can be! 

1. Write one of the numbers your multiplying above and the other number to the right of the chart, one digit per box. (Examples above: numbers 469 and 37)

2. Find the products for each cell of the chart. Use the 1-digit numbers on the outside of the chart as factors. Record each product in the cell with the tens digit of the product above the diagonal and the ones digit below. (Example above: 9x3=27, 9x7=63, and so on...)

3. Start at the lower right. Add diagonally as shown by the colored arrows. Write the ones digit of the diagonal sum below and to the left of the chart. IF the sum, along a diagonal is ten or more, regroup the 10 to the next diagonal. (Example above: 2+6+7=15, 2+8+4+8+(1)=23, etc)

4. Read the final product starting at the upper left digit, 1, from the top down and to the right (Example above: 17,353)

Now, this method may not work for everyone..But, there may be people out there like me that think this method is a lot easier and way more visual than figuring it out any other way. I am a visual learner so this helps me greatly! 

If you are still not understanding the lattice method I found a great video explaining the method a little more: 

                        

There  is a great website that helps you understand the different steps of the lattice method and how simple it is to learn and use. Here it is!

http://mathworld.wolfram.com/LatticeMethod.html

The lattice method is as simple as grabbing a pencil and paper, drawing a box, and writing a few numbers! I hope you all get the chance to use this method and see if it works for you, like it does for me! :) ENJOY!

Life without a calculator

Lets imagine life, for one second, without calculators. Scary, isn't it?! What would we do without them? We would ESTIMATE! It is very important for people of all ages to learn all about estimating and why its so important. First, I am going to share some important information with you that I learned this week in my college math class.

There are three main types of estimation:

1. Estimating the Quantity - finding how many students, days, lunches, classes, etc.
2. Estimating the Measure - finding how much length, area, volume, time, etc.
3. Estimating an Answer - finding a sum, difference, product, or quotient.

There are also many different techniques for estimating. I am going to share a few of my favorites with you. But, keep in mind...what works for some, doesn't always work for others! So experiment and see what works best for you! 

Rounding is based on locating the point halfway between consecutive multiples of 10, 100, 1000 and so on. So how would be round 208? You got it, 200!

Front end estimation is calculating the leftmost or "front end" digit of each number as if the remaining digits were all zeros. How would we front end estimate 258+365+102....200+300+100.

Clustering involves looking for the number about which the addends cluster and then multiplying by the number of addends. Take the numbers 48 55 47 52 and 53 for instance, we would cluster them around the number 50 and since there are 5 numbers that cluster around 50 you take 50 x 5 for your answer.

Now, your probably wondering why I am wasting your time telling you about these techniques. Well, I'm not. Now its time for a little story:

I was grocery shopping the other day with $100 (I give myself a budget because otherwise I go a little food crazy). While I was shopping I had to make sure I didn't go over my budget. So, while shopping I was using the rounding technique to make sure that I wasn't spending more then my limit. When I got the check-out, I still had $7 left over for extra money, but at least I didn't have to send something back because I was $7 over....we all know how embarrassing that is. This was made possible because I estimated how much each item cost. Brilliant, huh?!

Next time you think that estimating is a waste of time because we have calculators, remember...we don't always have calculators with us and we will need to know how to estimate our problems out.

Some more information on estimating is available at this website:
http://www.aaamath.com/est.htm

Still a little confused? Here is a great video with some examples on estimating and some more reasons on why estimating is so important! Enjoy!

Solving Problems

This week in math class I learned all about solving problems! I have always had a hard time with solving problems in math and this week I learned all about the basics. First, it helped for me to understand what exactly a problem is.

A problem is a situation for which the following conditions exist:

1. It involves a question that represents a challenge for the individual.
2. The question cannot be answered immediately by some routine procedure known to the individual.
3. The individual accepts the challenge. 

Second, I needed to understand what exactly problem solving is.

Problem Solving is a process by which an individual uses previously learned concepts, facts, and relationships, along with various reasoning skills and strategies to answer a question or questions about a situation. 

Third, I learned and understood the great problem solving model! Here is a little more information about the problem solving model that helped me learn all I needed to know about solving problems in math!

http://www-rohan.sdsu.edu/~ituba/math303s08/mathideas/mmi10_01_03.pdf

After learning all the basics of problem solving, I got to thinking...when will I use these strategies in real life?! I thought for a long time and even had a great discussion with my husband about it. I thought it would be fun to share some of the things we came up with! 

• Paying bills - figuring out how much money you will have to pay your bills and what you will have left over after. 
• Traveling - distance and time.
• Building - creating stuff for around your house (benches, shelves, etc.)
• Shopping - figuring out discounts, making sure you have the right amount of money, figuring out taxes, etc.
• Cooking - If you don't have the right amount of ingredients, how can you still make it work?! 
• Health - counting calories, how far you run, etc. 

After coming up with this list, I ended up using problem solving skills in many of these categories over my three day weekend. We payed bills when my husband got paid, went to a wedding and figured out how much we needed to spend on gas to get there, we went shopping for dress clothes and I got mine 20% off, and we also cooked cookies for fathers day but cut the recipe in half because there wasn't many people there. Problem solving is something that will come in handy every day of our lives, its just that  a lot of time we don't even notice that we use math strategies to figure them out!